Problem: Solve the system of equations. $\begin{aligned} & 13x-6y = 22 \\\\ & x=y+6 \end{aligned}$ $ x=$
Solution: We are given that ${x}={y+6}$. Let's substitute this expression into the first equation and solve for $y$ as follows: $\begin{aligned} 13{x}-6y &= 22\\\\ 13\cdot({y+6})-6y&=22\\\\ 13y+78-6y&=22\\\\ 7y&=-56\\\\ y&=-8 \end{aligned}$ Since we now know that ${y}={-8}$, we can substitute this value in the second equation to solve for $x$ as follows: $ \begin{aligned} x &= {y}+6 \\\\ x&={-8}+6\\\\ x&=-2 \end{aligned}$ This is the solution of the system: $\begin{aligned} &x = -2 \\\\ &y=-8 \end{aligned}$